More Applications of Percents

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1More Applications of Percents8-7More Applications of PercentsCourse 3Warm UpProblem of the DayLesson Presentation

2More Applications of PercentsCourse 38-7More Applications of PercentsWarm Up1. What is 35 increased by 8%?2. What is the percent of decrease from 144 to 120?3. What is 1500 decreased by 75%?4. What is the percent of increase from 0.32 to 0.64?37.816 %23375100%

3More Applications of PercentsCourse 38-7More Applications of PercentsProblem of the DayMaggie is running for class president. A poll revealed that 40% of her classmates have decided to vote for her, 32% have decided to vote for her opponent, and 7 voters are undecided. If she needs 50% of the vote to win, how many of the undecided voters must vote for Maggie for her to win the election?3

6More Applications of PercentsCourse 38-7More Applications of PercentsWhen you borrow money from a bank, you pay interest for the use of the bank’s money. When you deposit money into a savings account, you are paid interest. Simple interest is one type of fee paid for the use of money.Rate of interest is the percent charged or earnedSimple InterestI = P  r  tTime that the money is borrowed or invested (in years)Principal is the amount of money borrowed or invested

7Additional Example 1: Finding Interest and Total Payment on a LoanCourse 38-7More Applications of PercentsAdditional Example 1: Finding Interest and Total Payment on a LoanTo buy a car, Jessica borrowed $15,000 for 3 years at an annual simple interest rate of 9%. How much interest will she pay if she pays the entire loan off at the end of the third year? What is the total amount that she will repay?First, find the interest she will pay.I = P  r  t Use the formula.I = 15,000  0.09  3 Substitute. Use 0.09 for 9%.I = Solve for I.

8Additional Example 1 ContinuedCourse 38-7More Applications of PercentsAdditional Example 1 ContinuedJessica will pay $4050 in interest.You can find the total amount A to be repaid on a loan by adding the principal P to the interest I.P + I = A principal + interest = amount15, = A Substitute.19,050 = A Solve for A.Jessica will repay a total of $19,050 on her loan.

9More Applications of PercentsCourse 38-7More Applications of PercentsTry This: Example 1To buy a laptop computer, Elaine borrowed $2,000 for 3 years at an annual simple interest rate of 5%. How much interest will she pay if she pays the entire loan off at the end of the third year? What is the total amount that she will repay?First, find the interest she will pay.I = P  r  t Use the formula.I = 2,000  0.05  3 Substitute. Use 0.05 for 5%.I = Solve for I.

10Try This: Example 1 ContinuedCourse 38-7More Applications of PercentsTry This: Example 1 ContinuedElaine will pay $300 in interest.You can find the total amount A to be repaid on a loan by adding the principal P to the interest I.P + I = A principal + interest = amount= A Substitute.2300 = A Solve for A.Elaine will repay a total of $2300 on her loan.

11Additional Example 2: Determining the Amount of Investment TimeCourse 38-7More Applications of PercentsAdditional Example 2: Determining the Amount of Investment TimeNancy invested $6000 in a bond at a yearly rate of 3%. She earned $450 in interest. How long was the money invested?I = P  r  t Use the formula.450 = 6,000  0.03  t Substitute values into the equation.450 = 180t2.5 = t Solve for t.The money was invested for 2.5 years, or 2 years and 6 months.

12More Applications of PercentsCourse 38-7More Applications of PercentsTry This: Example 2TJ invested $4000 in a bond at a yearly rate of 2%. He earned $200 in interest. How long was the money invested?I = P  r  t Use the formula.200 = 4,000  0.02  t Substitute values into the equation.200 = 80t2.5 = t Solve for t.The money was invested for 2.5 years, or 2 years and 6 months.

13Additional Example 3: Computing Total SavingsCourse 38-7More Applications of PercentsAdditional Example 3: Computing Total SavingsJohn’s parents deposited $1000 into a savings account as a college fund when he was born. How much will John have in this account after 18 years at a yearly simple interest rate of 3.25%?I = P  r  t Use the formula.I = 1000   Substitute. Use for 3.25%.I = Solve for I.Now you can find the total.

14Additional Example 3 ContinuedCourse 38-7More Applications of PercentsAdditional Example 3 ContinuedP + I = A Use the formula.= A1585 = AJohn will have $1585 in the account after 18 years.

15More Applications of PercentsCourse 38-7More Applications of PercentsTry This: Example 3Bertha deposited $1000 into a retirement account when she was 18. How much will Bertha have in this account after 50 years at a yearly simple interest rate of 7.5%?I = P  r  t Use the formula.I = 1000   Substitute. Use for 7.5%.I = Solve for I.Now you can find the total.

16Try This: Example 3 ContinuedCourse 38-7More Applications of PercentsTry This: Example 3 ContinuedP + I = A Use the formula.= A4750 = ABertha will have $4750 in the account after 50 years.

17Additional Example 4: Finding the Rate of InterestCourse 38-7More Applications of PercentsAdditional Example 4: Finding the Rate of InterestMr. Johnson borrowed $8000 for 4 years to make home improvements. If he repaid a total of $10,320, at what interest rate did he borrow the money?P + I = A Use the formula.I = 10,320I = 10,320 – 8000 = 2320 Find the amount of interest.He paid $2320 in interest. Use the amount of interest to find the interest rate.

19More Applications of PercentsCourse 38-7More Applications of PercentsTry This: Example 4Mr. Mogi borrowed $9000 for 10 years to make home improvements. If he repaid a total of $20,000 at what interest rate did he borrow the money?P + I = A Use the formula.I = 20,000I = 20,000 – 9000 = 11,000 Find the amount of interest.He paid $11,000 in interest. Use the amount of interest to find the interest rate.

21More Applications of Percents Insert Lesson Title HereCourse 38-7More Applications of PercentsInsert Lesson Title HereLesson Quiz: Part 11. A bank is offering 2.5% simple interest on a savings account. If you deposit $5000, how much interest will you earn in one year?2. Joshua borrowed $1000 from his friend and paid him back $1050 in six months. What simple annual interest did Joshua pay his friend?$12510%

22More Applications of Percents Insert Lesson Title HereCourse 38-7More Applications of PercentsInsert Lesson Title HereLesson Quiz: Part 23. The Hemmings borrowed $3000 for home improvements. They repaid the loan and $600 in simple interest four years later. What simple annual interest rate did they pay?4. Mr. Berry had $120,000 in a retirement account. The account paid 4.25% simple interest. How much money was in the account at the end of 10 years?5%$171,000